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Eigenfunction expansions of ultradifferentiable functions and ultradistributions


Authors: Aparajita Dasgupta and Michael Ruzhansky
Journal: Trans. Amer. Math. Soc. 368 (2016), 8481-8498
MSC (2010): Primary 46F05; Secondary 22E30
Published electronically: January 14, 2016
MathSciNet review: 3551578
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Abstract: In this paper we give a global characterisation of classes of ultradifferentiable functions and corresponding ultradistributions on a compact manifold $ X$. The characterisation is given in terms of the eigenfunction expansion of an elliptic operator on $ X$. This extends the result for analytic functions on compact manifolds by Seeley in 1969, and the characterisation of Gevrey functions and Gevrey ultradistributions on compact Lie groups and homogeneous spaces by the authors (2014).


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Additional Information

Aparajita Dasgupta
Affiliation: Faculté des Sciences, École polytechnique fédérale de Lausanne, CH-1015 Lausanne, Switzerland
Email: aparajita.dasgupta@epfl.ch

Michael Ruzhansky
Affiliation: Department of Mathematics, Imperial College London, 180 Queen’s Gate, London SW7 2AZ, United Kingdom
Email: m.ruzhansky@imperial.ac.uk

DOI: https://doi.org/10.1090/tran/6765
Keywords: Gevrey spaces, ultradistributions, Komatsu classes
Received by editor(s): October 9, 2014
Published electronically: January 14, 2016
Additional Notes: The second author was supported by the EPSRC Grant EP/K039407/1 and by the Leverhulme Research Grant RPG-2014-02.
Dedicated: Dedicated to the memory of Todor Gramchev (1956-2015)
Article copyright: © Copyright 2016 American Mathematical Society